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<title>itab.c</title>
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<tt><b><i>/*&nbsp;Table&nbsp;of&nbsp;integrals</tt><br>
<tt></tt><br>
<tt>The&nbsp;symbol&nbsp;f&nbsp;is&nbsp;just&nbsp;a&nbsp;dummy&nbsp;symbol&nbsp;for&nbsp;creating&nbsp;a&nbsp;list&nbsp;f(A,B,C,C,...)&nbsp;where</tt><br>
<tt></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;A&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;is&nbsp;the&nbsp;template&nbsp;expression</tt><br>
<tt></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;B&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;is&nbsp;the&nbsp;result&nbsp;expression</tt><br>
<tt></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;C&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;is&nbsp;an&nbsp;optional&nbsp;list&nbsp;of&nbsp;conditional&nbsp;expressions</tt><br>
<tt>*/</i></b></tt><br>
<tt></tt><br>
<tt>#include&nbsp;"defs.h"</tt><br>
<tt></tt><br>
<tt>const&nbsp;char&nbsp;*itab[]&nbsp;=&nbsp;{</tt><br>
<tt><b><i>//&nbsp;1</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(a,a*x)",</tt><br>
<tt><b><i>//&nbsp;9&nbsp;(need&nbsp;a&nbsp;caveat&nbsp;for&nbsp;7&nbsp;so&nbsp;we&nbsp;can&nbsp;put&nbsp;9&nbsp;after&nbsp;7)</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/x,log(x))",</tt><br>
<tt><b><i>//&nbsp;7</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x^a,x^(a+1)/(a+1))",</tt><br>
<tt><b><i>//&nbsp;12</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(exp(a*x),1/a*exp(a*x))",</tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(exp(a*x+b),1/a*exp(a*x+b))",</tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x*exp(a*x^2),exp(a*x^2)/(2*a))",</tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x*exp(a*x^2+b),exp(a*x^2+b)/(2*a))",</tt><br>
<tt><b><i>//&nbsp;14</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(log(a*x),x*log(a*x)-x)",</tt><br>
<tt><b><i>//&nbsp;15</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(a^x,a^x/log(a),or(not(number(a)),a&gt;0))",</tt><br>
<tt><b><i>//&nbsp;16</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/(a+x^2),1/sqrt(a)*arctan(x/sqrt(a)),or(not(number(a)),a&gt;0))",</tt><br>
<tt><b><i>//&nbsp;17</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/(a-x^2),1/sqrt(a)*arctanh(x/sqrt(a)))",</tt><br>
<tt><b><i>//&nbsp;19</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/sqrt(a-x^2),arcsin(x/(sqrt(a))))",</tt><br>
<tt><b><i>//&nbsp;20</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/sqrt(a+x^2),log(x+sqrt(a+x^2)))",</tt><br>
<tt><b><i>//&nbsp;27</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/(a+b*x),1/b*log(a+b*x))",</tt><br>
<tt><b><i>//&nbsp;28</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/(a+b*x)^2,-1/(b*(a+b*x)))",</tt><br>
<tt><b><i>//&nbsp;29</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/(a+b*x)^3,-1/(2*b)*1/(a+b*x)^2)",</tt><br>
<tt><b><i>//&nbsp;30</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x/(a+b*x),x/b-a*log(a+b*x)/b/b)",</tt><br>
<tt><b><i>//&nbsp;31</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x/(a+b*x)^2,1/b^2*(log(a+b*x)+a/(a+b*x)))",</tt><br>
<tt><b><i>//&nbsp;33</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x^2/(a+b*x),1/b^2*(1/2*(a+b*x)^2-2*a*(a+b*x)+a^2*log(a+b*x)))",</tt><br>
<tt><b><i>//&nbsp;34</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x^2/(a+b*x)^2,1/b^3*(a+b*x-2*a*log(a+b*x)-a^2/(a+b*x)))",</tt><br>
<tt><b><i>//&nbsp;35</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x^2/(a+b*x)^3,1/b^3*(log(a+b*x)+2*a/(a+b*x)-1/2*a^2/(a+b*x)^2))",</tt><br>
<tt><b><i>//&nbsp;37</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/x*1/(a+b*x),-1/a*log((a+b*x)/x))",</tt><br>
<tt><b><i>//&nbsp;38</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/x*1/(a+b*x)^2,1/a*1/(a+b*x)-1/a^2*log((a+b*x)/x))",</tt><br>
<tt><b><i>//&nbsp;39</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/x*1/(a+b*x)^3,1/a^3*(1/2*((2*a+b*x)/(a+b*x))^2+log(x/(a+b*x))))",</tt><br>
<tt><b><i>//&nbsp;40</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/x^2*1/(a+b*x),-1/(a*x)+b/a^2*log((a+b*x)/x))",</tt><br>
<tt><b><i>//&nbsp;41</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/x^3*1/(a+b*x),(2*b*x-a)/(2*a^2*x^2)+b^2/a^3*log(x/(a+b*x)))",</tt><br>
<tt><b><i>//&nbsp;42</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/x^2*1/(a+b*x)^2,-(a+2*b*x)/(a^2*x*(a+b*x))+2*b/a^3*log((a+b*x)/x))",</tt><br>
<tt><b><i>//&nbsp;60</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/(a+b*x^2),1/sqrt(a*b)*arctan(x*sqrt(a*b)/a),or(not(number(a*b)),a*b&gt;0))",</tt><br>
<tt><b><i>//&nbsp;61</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/(a+b*x^2),1/(2*sqrt(-a*b))*log((a+x*sqrt(-a*b))/(a-x*sqrt(-a*b))),or(not(number(a*b)),a*b&lt;0))",</tt><br>
<tt><b><i>//&nbsp;62&nbsp;is&nbsp;the&nbsp;same&nbsp;as&nbsp;60</i></b></tt><br>
<tt><b><i>//&nbsp;63</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x/(a+b*x^2),1/2*1/b*log(a+b*x^2))",</tt><br>
<tt><b><i>//64</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x^2/(a+b*x^2),x/b-a/b*integral(1/(a+b*x^2),x))",</tt><br>
<tt><b><i>//65</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/(a+b*x^2)^2,x/(2*a*(a+b*x^2))+1/2*1/a*integral(1/(a+b*x^2),x))",</tt><br>
<tt><b><i>//66&nbsp;is&nbsp;covered&nbsp;by&nbsp;61</i></b></tt><br>
<tt><b><i>//70</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/x*1/(a+b*x^2),1/2*1/a*log(x^2/(a+b*x^2)))",</tt><br>
<tt><b><i>//71</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/x^2*1/(a+b*x^2),-1/(a*x)-b/a*integral(1/(a+b*x^2),x))",</tt><br>
<tt><b><i>//74</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/(a+b*x^3),1/3*1/a*(a/b)^(1/3)*(1/2*log(((a/b)^(1/3)+x)^3/(a+b*x^3))+sqrt(3)*arctan((2*x-(a/b)^(1/3))*(a/b)^(-1/3)/sqrt(3))))",</tt><br>
<tt><b><i>//76</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x^2/(a+b*x^3),1/3*1/b*log(a+b*x^3))",</tt><br>
<tt><b><i>//77</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/(a+b*x^4),1/2*1/a*(a/b/4)^(1/4)*(1/2*log((x^2+2*(a/b/4)^(1/4)*x+2*(a/b/4)^(1/2))/(x^2-2*(a/b/4)^(1/4)*x+2*(a/b/4)^(1/2)))+arctan(2*(a/b/4)^(1/4)*x/(2*(a/b/4)^(1/2)-x^2))),or(not(number(a*b)),a*b&gt;0))",</tt><br>
<tt><b><i>//78</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/(a+b*x^4),1/2*(-a/b)^(1/4)/a*(1/2*log((x+(-a/b)^(1/4))/(x-(-a/b)^(1/4)))+arctan(x*(-a/b)^(-1/4))),or(not(number(a*b)),a*b&lt;0))",</tt><br>
<tt><b><i>//79</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x/(a+b*x^4),1/2*sqrt(b/a)/b*arctan(x^2*sqrt(b/a)),or(not(number(a*b)),a*b&gt;0))",</tt><br>
<tt><b><i>//80</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x/(a+b*x^4),1/4*sqrt(-b/a)/b*log((x^2-sqrt(-a/b))/(x^2+sqrt(-a/b))),or(not(number(a*b)),a*b&lt;0))",</tt><br>
<tt><b><i>//81</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x^2/(a+b*x^4),1/4*1/b*(a/b/4)^(-1/4)*(1/2*log((x^2-2*(a/b/4)^(1/4)*x+2*sqrt(a/b/4))/(x^2+2*(a/b/4)^(1/4)*x+2*sqrt(a/b/4)))+arctan(2*(a/b/4)^(1/4)*x/(2*sqrt(a/b/4)-x^2))),or(not(number(a*b)),a*b&gt;0))",</tt><br>
<tt><b><i>//82</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x^2/(a+b*x^4),1/4*1/b*(-a/b)^(-1/4)*(log((x-(-a/b)^(1/4))/(x+(-a/b)^(1/4)))+2*arctan(x*(-a/b)^(-1/4))),or(not(number(a*b)),a*b&lt;0))",</tt><br>
<tt><b><i>//83</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x^3/(a+b*x^4),1/4*1/b*log(a+b*x^4))",</tt><br>
<tt><b><i>//124</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(sqrt(a+b*x),2/3*1/b*sqrt((a+b*x)^3))",</tt><br>
<tt><b><i>//125</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x*sqrt(a+b*x),-2*(2*a-3*b*x)*sqrt((a+b*x)^3)/15/b^2)",</tt><br>
<tt><b><i>//126</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x^2*sqrt(a+b*x),2*(8*a^2-12*a*b*x+15*b^2*x^2)*sqrt((a+b*x)^3)/105/b^3)",</tt><br>
<tt><b><i>//128</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(sqrt(a+b*x)/x,2*sqrt(a+b*x)+a*integral(1/x*1/sqrt(a+b*x),x))",</tt><br>
<tt><b><i>//129</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(sqrt(a+b*x)/x^2,-sqrt(a+b*x)/x+b/2*integral(1/x*1/sqrt(a+b*x),x))",</tt><br>
<tt><b><i>//131</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/sqrt(a+b*x),2*sqrt(a+b*x)/b)",</tt><br>
<tt><b><i>//132</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x/sqrt(a+b*x),-2/3*(2*a-b*x)*sqrt(a+b*x)/b^2)",</tt><br>
<tt><b><i>//133</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x^2/sqrt(a+b*x),2/15*(8*a^2-4*a*b*x+3*b^2*x^2)*sqrt(a+b*x)/b^3)",</tt><br>
<tt><b><i>//135</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/x*1/sqrt(a+b*x),1/sqrt(a)*log((sqrt(a+b*x)-sqrt(a))/(sqrt(a+b*x)+sqrt(a))),or(not(number(a)),a&gt;0))",</tt><br>
<tt><b><i>//136</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/x*1/sqrt(a+b*x),2/sqrt(-a)*arctan(sqrt(-(a+b*x)/a)),or(not(number(a)),a&lt;0))",</tt><br>
<tt><b><i>//137</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/x^2*1/sqrt(a+b*x),-sqrt(a+b*x)/a/x-1/2*b/a*integral(1/x*1/sqrt(a+b*x),x))",</tt><br>
<tt><b><i>//156</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(sqrt(x^2+a),1/2*(x*sqrt(x^2+a)+a*log(x+sqrt(x^2+a))))",</tt><br>
<tt><b><i>//157</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/sqrt(x^2+a),log(x+sqrt(x^2+a)))",</tt><br>
<tt><b><i>//158</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/x*1/sqrt(x^2+a),arcsec(x/sqrt(-a))/sqrt(-a),or(not(number(a)),a&lt;0))",</tt><br>
<tt><b><i>//159</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/x*1/sqrt(x^2+a),-1/sqrt(a)*log((sqrt(a)+sqrt(x^2+a))/x),or(not(number(a)),a&gt;0))",</tt><br>
<tt><b><i>//160</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(sqrt(x^2+a)/x,sqrt(x^2+a)-sqrt(a)*log((sqrt(a)+sqrt(x^2+a))/x),or(not(number(a)),a&gt;0))",</tt><br>
<tt><b><i>//161</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(sqrt(x^2+a)/x,sqrt(x^2+a)-sqrt(-a)*arcsec(x/sqrt(-a)),or(not(number(a)),a&lt;0))",</tt><br>
<tt><b><i>//162</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x/sqrt(x^2+a),sqrt(x^2+a))",</tt><br>
<tt><b><i>//163</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x*sqrt(x^2+a),1/3*sqrt((x^2+a)^3))",</tt><br>
<tt><b><i>//164&nbsp;need&nbsp;an&nbsp;unexpanded&nbsp;version?</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(sqrt(a+x^6+3*a^(1/3)*x^4+3*a^(2/3)*x^2),1/4*(x*sqrt((x^2+a^(1/3))^3)+3/2*a^(1/3)*x*sqrt(x^2+a^(1/3))+3/2*a^(2/3)*log(x+sqrt(x^2+a^(1/3)))))",</tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<b><i>//&nbsp;match&nbsp;doesn't&nbsp;work&nbsp;for&nbsp;the&nbsp;following</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(sqrt(-a+x^6-3*a^(1/3)*x^4+3*a^(2/3)*x^2),1/4*(x*sqrt((x^2-a^(1/3))^3)-3/2*a^(1/3)*x*sqrt(x^2-a^(1/3))+3/2*a^(2/3)*log(x+sqrt(x^2-a^(1/3)))))",</tt><br>
<tt><b><i>//165</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/sqrt(a+x^6+3*a^(1/3)*x^4+3*a^(2/3)*x^2),x/a^(1/3)/sqrt(x^2+a^(1/3)))",</tt><br>
<tt><b><i>//166</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x/sqrt(a+x^6+3*a^(1/3)*x^4+3*a^(2/3)*x^2),-1/sqrt(x^2+a^(1/3)))",</tt><br>
<tt><b><i>//167</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x*sqrt(a+x^6+3*a^(1/3)*x^4+3*a^(2/3)*x^2),1/5*sqrt((x^2+a^(1/3))^5))",</tt><br>
<tt><b><i>//168</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x^2*sqrt(x^2+a),1/4*x*sqrt((x^2+a)^3)-1/8*a*x*sqrt(x^2+a)-1/8*a^2*log(x+sqrt(x^2+a)))",</tt><br>
<tt><b><i>//169</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x^3*sqrt(x^2+a),(1/5*x^2-2/15*a)*sqrt((x^2+a)^3),and(number(a),a&gt;0))",</tt><br>
<tt><b><i>//170</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x^3*sqrt(x^2+a),sqrt((x^2+a)^5)/5-a*sqrt((x^2+a)^3)/3,and(number(a),a&lt;0))",</tt><br>
<tt><b><i>//171</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x^2/sqrt(x^2+a),1/2*x*sqrt(x^2+a)-1/2*a*log(x+sqrt(x^2+a)))",</tt><br>
<tt><b><i>//172</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x^3/sqrt(x^2+a),1/3*sqrt((x^2+a)^3)-a*sqrt(x^2+a))",</tt><br>
<tt><b><i>//173</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/x^2*1/sqrt(x^2+a),-sqrt(x^2+a)/a/x)",</tt><br>
<tt><b><i>//174</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/x^3*1/sqrt(x^2+a),-1/2*sqrt(x^2+a)/a/x^2+1/2*log((sqrt(a)+sqrt(x^2+a))/x)/a^(3/2),or(not(number(a)),a&gt;0))",</tt><br>
<tt><b><i>//175</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/x^3*1/sqrt(x^2-a),1/2*sqrt(x^2-a)/a/x^2+1/2*1/(a^(3/2))*arcsec(x/(a^(1/2))),or(not(number(a)),a&gt;0))",</tt><br>
<tt><b><i>//176+</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x^2*sqrt(a+x^6+3*a^(1/3)*x^4+3*a^(2/3)*x^2),1/6*x*sqrt((x^2+a^(1/3))^5)-1/24*a^(1/3)*x*sqrt((x^2+a^(1/3))^3)-1/16*a^(2/3)*x*sqrt(x^2+a^(1/3))-1/16*a*log(x+sqrt(x^2+a^(1/3))),or(not(number(a)),a&gt;0))",</tt><br>
<tt><b><i>//176-</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x^2*sqrt(-a-3*a^(1/3)*x^4+3*a^(2/3)*x^2+x^6),1/6*x*sqrt((x^2-a^(1/3))^5)+1/24*a^(1/3)*x*sqrt((x^2-a^(1/3))^3)-1/16*a^(2/3)*x*sqrt(x^2-a^(1/3))+1/16*a*log(x+sqrt(x^2-a^(1/3))),or(not(number(a)),a&gt;0))",</tt><br>
<tt><b><i>//177+</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x^3*sqrt(a+x^6+3*a^(1/3)*x^4+3*a^(2/3)*x^2),1/7*sqrt((x^2+a^(1/3))^7)-1/5*a^(1/3)*sqrt((x^2+a^(1/3))^5),or(not(number(a)),a&gt;0))",</tt><br>
<tt><b><i>//177-</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x^3*sqrt(-a-3*a^(1/3)*x^4+3*a^(2/3)*x^2+x^6),1/7*sqrt((x^2-a^(1/3))^7)+1/5*a^(1/3)*sqrt((x^2-a^(1/3))^5),or(not(number(a)),a&gt;0))",</tt><br>
<tt><b><i>//196</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/(x-a)/sqrt(x^2-a^2),-sqrt(x^2-a^2)/a/(x-a))",</tt><br>
<tt><b><i>//197</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/(x+a)/sqrt(x^2-a^2),sqrt(x^2-a^2)/a/(x+a))",</tt><br>
<tt><b><i>//200+</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(sqrt(a-x^2),1/2*(x*sqrt(a-x^2)+a*arcsin(x/sqrt(abs(a)))))",</tt><br>
<tt><b><i>//201&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(seems&nbsp;to&nbsp;be&nbsp;handled&nbsp;somewhere&nbsp;else)</i></b></tt><br>
<tt><b><i>//202</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/x*1/sqrt(a-x^2),-1/sqrt(a)*log((sqrt(a)+sqrt(a-x^2))/x),or(not(number(a)),a&gt;0))",</tt><br>
<tt><b><i>//203</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(sqrt(a-x^2)/x,sqrt(a-x^2)-sqrt(a)*log((sqrt(a)+sqrt(a-x^2))/x),or(not(number(a)),a&gt;0))",</tt><br>
<tt><b><i>//204</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x/sqrt(a-x^2),-sqrt(a-x^2))",</tt><br>
<tt><b><i>//205</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x*sqrt(a-x^2),-1/3*sqrt((a-x^2)^3))",</tt><br>
<tt><b><i>//210</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x^2*sqrt(a-x^2),-x/4*sqrt((a-x^2)^3)+1/8*a*(x*sqrt(a-x^2)+a*arcsin(x/sqrt(a))),or(not(number(a)),a&gt;0))",</tt><br>
<tt><b><i>//211</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x^3*sqrt(a-x^2),(-1/5*x^2-2/15*a)*sqrt((a-x^2)^3),or(not(number(a)),a&gt;0))",</tt><br>
<tt><b><i>//214</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x^2/sqrt(a-x^2),-x/2*sqrt(a-x^2)+a/2*arcsin(x/sqrt(a)),or(not(number(a)),a&gt;0))",</tt><br>
<tt><b><i>//215</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/x^2*1/sqrt(a-x^2),-sqrt(a-x^2)/a/x,or(not(number(a)),a&gt;0))",</tt><br>
<tt><b><i>//216</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(sqrt(a-x^2)/x^2,-sqrt(a-x^2)/x-arcsin(x/sqrt(a)),or(not(number(a)),a&gt;0))",</tt><br>
<tt><b><i>//217</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(sqrt(a-x^2)/x^3,-1/2*sqrt(a-x^2)/x^2+1/2*log((sqrt(a)+sqrt(a-x^2))/x)/sqrt(a),or(not(number(a)),a&gt;0))",</tt><br>
<tt><b><i>//218</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(sqrt(a-x^2)/x^4,-1/3*sqrt((a-x^2)^3)/a/x^3,or(not(number(a)),a&gt;0))",</tt><br>
<tt><b><i>//&nbsp;273</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(sqrt(a*x^2+b),x*sqrt(a*x^2+b)/2+b*log(x*sqrt(a)+sqrt(a*x^2+b))/2/sqrt(a),and(number(a),a&gt;0))",</tt><br>
<tt><b><i>//&nbsp;274</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(sqrt(a*x^2+b),x*sqrt(a*x^2+b)/2+b*arcsin(x*sqrt(-a/b))/2/sqrt(-a),and(number(a),a&lt;0))",</tt><br>
<tt><b><i>//&nbsp;290</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(sin(a*x),-cos(a*x)/a)",</tt><br>
<tt><b><i>//&nbsp;291</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(cos(a*x),sin(a*x)/a)",</tt><br>
<tt><b><i>//&nbsp;292</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(tan(a*x),-log(cos(a*x))/a)",</tt><br>
<tt><b><i>//&nbsp;293</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/tan(a*x),log(sin(a*x))/a)",</tt><br>
<tt><b><i>//&nbsp;294</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/cos(a*x),log(tan(pi/4+a*x/2))/a)",</tt><br>
<tt><b><i>//&nbsp;295</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/sin(a*x),log(tan(a*x/2))/a)",</tt><br>
<tt><b><i>//&nbsp;296</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(sin(a*x)^2,x/2-sin(2*a*x)/(4*a))",</tt><br>
<tt><b><i>//&nbsp;297</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(sin(a*x)^3,-cos(a*x)*(sin(a*x)^2+2)/(3*a))",</tt><br>
<tt><b><i>//&nbsp;298</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(sin(a*x)^4,3/8*x-sin(2*a*x)/(4*a)+sin(4*a*x)/(32*a))",</tt><br>
<tt><b><i>//&nbsp;302</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(cos(a*x)^2,x/2+sin(2*a*x)/(4*a))",</tt><br>
<tt><b><i>//&nbsp;303</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(cos(a*x)^3,sin(a*x)*(cos(a*x)^2+2)/(3*a))",</tt><br>
<tt><b><i>//&nbsp;304</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(cos(a*x)^4,3/8*x+sin(2*a*x)/(4*a)+sin(4*a*x)/(32*a))",</tt><br>
<tt><b><i>//&nbsp;308</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/sin(a*x)^2,-1/(a*tan(a*x)))",</tt><br>
<tt><b><i>//&nbsp;312</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/cos(a*x)^2,tan(a*x)/a)",</tt><br>
<tt><b><i>//&nbsp;318</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(sin(a*x)*cos(a*x),sin(a*x)^2/(2*a))",</tt><br>
<tt><b><i>//&nbsp;320</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(sin(a*x)^2*cos(a*x)^2,-sin(4*a*x)/(32*a)+x/8)",</tt><br>
<tt><b><i>//&nbsp;326</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(sin(a*x)/cos(a*x)^2,1/(a*cos(a*x)))",</tt><br>
<tt><b><i>//&nbsp;327</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(sin(a*x)^2/cos(a*x),(log(tan(pi/4+a*x/2))-sin(a*x))/a)",</tt><br>
<tt><b><i>//&nbsp;328</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(cos(a*x)/sin(a*x)^2,-1/(a*sin(a*x)))",</tt><br>
<tt><b><i>//&nbsp;329</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/(sin(a*x)*cos(a*x)),log(tan(a*x))/a)",</tt><br>
<tt><b><i>//&nbsp;330</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/(sin(a*x)*cos(a*x)^2),(1/cos(a*x)+log(tan(a*x/2)))/a)",</tt><br>
<tt><b><i>//&nbsp;331</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/(sin(a*x)^2*cos(a*x)),(log(tan(pi/4+a*x/2))-1/sin(a*x))/a)",</tt><br>
<tt><b><i>//&nbsp;333</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/(sin(a*x)^2*cos(a*x)^2),-2/(a*tan(2*a*x)))",</tt><br>
<tt><b><i>//&nbsp;335</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(sin(a+b*x),-cos(a+b*x)/b)",</tt><br>
<tt><b><i>//&nbsp;336</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(cos(a+b*x),sin(a+b*x)/b)",</tt><br>
<tt><b><i>//&nbsp;337+&nbsp;(with&nbsp;the&nbsp;addition&nbsp;of&nbsp;b)</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/(b+b*sin(a*x)),-tan(pi/4-a*x/2)/a/b)",</tt><br>
<tt><b><i>//&nbsp;337-&nbsp;(with&nbsp;the&nbsp;addition&nbsp;of&nbsp;b)</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/(b-b*sin(a*x)),tan(pi/4+a*x/2)/a/b)",</tt><br>
<tt><b><i>//&nbsp;338&nbsp;(with&nbsp;the&nbsp;addition&nbsp;of&nbsp;b)</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/(b+b*cos(a*x)),tan(a*x/2)/a/b)",</tt><br>
<tt><b><i>//&nbsp;339&nbsp;(with&nbsp;the&nbsp;addition&nbsp;of&nbsp;b)</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/(b-b*cos(a*x)),-1/tan(a*x/2)/a/b)",</tt><br>
<tt><b><i>//&nbsp;340</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/(a+b*sin(x)),1/sqrt(b^2-a^2)*log((a*tan(x/2)+b-sqrt(b^2-a^2))/(a*tan(x/2)+b+sqrt(b^2-a^2))),b^2-a^2)",&nbsp;<b><i>//&nbsp;check&nbsp;that&nbsp;b^2-a^2&nbsp;is&nbsp;not&nbsp;zero</i></b></tt><br>
<tt><b><i>//&nbsp;341</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/(a+b*cos(x)),1/sqrt(b^2-a^2)*log((sqrt(b^2-a^2)*tan(x/2)+a+b)/(sqrt(b^2-a^2)*tan(x/2)-a-b)),b^2-a^2)",&nbsp;<b><i>//&nbsp;check&nbsp;that&nbsp;b^2-a^2&nbsp;is&nbsp;not&nbsp;zero</i></b></tt><br>
<tt><b><i>//&nbsp;389</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x*sin(a*x),sin(a*x)/a^2-x*cos(a*x)/a)",</tt><br>
<tt><b><i>//&nbsp;390</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x^2*sin(a*x),2*x*sin(a*x)/a^2-(a^2*x^2-2)*cos(a*x)/a^3)",</tt><br>
<tt><b><i>//&nbsp;393</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x*cos(a*x),cos(a*x)/a^2+x*sin(a*x)/a)",</tt><br>
<tt><b><i>//&nbsp;394</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x^2*cos(a*x),2*x*cos(a*x)/a^2+(a^2*x^2-2)*sin(a*x)/a^3)",</tt><br>
<tt><b><i>//&nbsp;441</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(arcsin(a*x),x*arcsin(a*x)+sqrt(1-a^2*x^2)/a)",</tt><br>
<tt><b><i>//&nbsp;442</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(arccos(a*x),x*arccos(a*x)+sqrt(1-a^2*x^2)/a)",</tt><br>
<tt><b><i>//&nbsp;443</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(arctan(a*x),x*arctan(a*x)-1/2*log(1+a^2*x^2)/a)",</tt><br>
<tt><b><i>//&nbsp;485&nbsp;(with&nbsp;addition&nbsp;of&nbsp;a)</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(log(a*x),x*log(a*x)-x)",</tt><br>
<tt><b><i>//&nbsp;486&nbsp;(with&nbsp;addition&nbsp;of&nbsp;a)</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x*log(a*x),x^2*log(a*x)/2-x^2/4)",</tt><br>
<tt><b><i>//&nbsp;487&nbsp;(with&nbsp;addition&nbsp;of&nbsp;a)</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x^2*log(a*x),x^3*log(a*x)/3-1/9*x^3)",</tt><br>
<tt><b><i>//&nbsp;489</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(log(x)^2,x*log(x)^2-2*x*log(x)+2*x)",</tt><br>
<tt><b><i>//&nbsp;493&nbsp;(with&nbsp;addition&nbsp;of&nbsp;a)</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(1/x*1/(a+log(x)),log(a+log(x)))",</tt><br>
<tt><b><i>//&nbsp;499</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(log(a*x+b),(a*x+b)*log(a*x+b)/a-x)",</tt><br>
<tt><b><i>//&nbsp;500</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(log(a*x+b)/x^2,a/b*log(x)-(a*x+b)*log(a*x+b)/b/x)",</tt><br>
<tt><b><i>//&nbsp;554</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(sinh(x),cosh(x))",</tt><br>
<tt><b><i>//&nbsp;555</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(cosh(x),sinh(x))",</tt><br>
<tt><b><i>//&nbsp;556</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(tanh(x),log(cosh(x)))",</tt><br>
<tt><b><i>//&nbsp;560</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x*sinh(x),x*cosh(x)-sinh(x))",</tt><br>
<tt><b><i>//&nbsp;562</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x*cosh(x),x*sinh(x)-cosh(x))",</tt><br>
<tt><b><i>//&nbsp;566</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(sinh(x)^2,sinh(2*x)/4-x/2)",</tt><br>
<tt><b><i>//&nbsp;569</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(tanh(x)^2,x-tanh(x))",</tt><br>
<tt><b><i>//&nbsp;572</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(cosh(x)^2,sinh(2*x)/4+x/2)",</tt><br>
<tt><b><i>//&nbsp;?</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x^3*exp(a*x^2),exp(a*x^2)*(x^2/a-1/(a^2))/2)",</tt><br>
<tt><b><i>//&nbsp;?</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x^3*exp(a*x^2+b),exp(a*x^2)*exp(b)*(x^2/a-1/(a^2))/2)",</tt><br>
<tt><b><i>//&nbsp;?</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(exp(a*x^2),-i*sqrt(pi)*erf(i*sqrt(a)*x)/sqrt(a)/2)",</tt><br>
<tt><b><i>//&nbsp;?</i></b></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(erf(a*x),x*erf(a*x)+exp(-a^2*x^2)/a/sqrt(pi))",</tt><br>
<tt></tt><br>
<tt><b><i>//&nbsp;these&nbsp;are&nbsp;needed&nbsp;for&nbsp;the&nbsp;surface&nbsp;integral&nbsp;in&nbsp;the&nbsp;manual</i></b></tt><br>
<tt></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x^2*(1-x^2)^(3/2),(x*sqrt(1-x^2)*(-8*x^4+14*x^2-3)+3*arcsin(x))/48)",</tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x^2*(1-x^2)^(5/2),(x*sqrt(1-x^2)*(48*x^6-136*x^4+118*x^2-15)+15*arcsin(x))/384)",</tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x^4*(1-x^2)^(3/2),(-x*sqrt(1-x^2)*(16*x^6-24*x^4+2*x^2+3)+3*arcsin(x))/128)",</tt><br>
<tt></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x*exp(a*x),exp(a*x)*(a*x-1)/(a^2))",</tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x*exp(a*x+b),exp(a*x+b)*(a*x-1)/(a^2))",</tt><br>
<tt></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x^2*exp(a*x),exp(a*x)*(a^2*x^2-2*a*x+2)/(a^3))",</tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x^2*exp(a*x+b),exp(a*x+b)*(a^2*x^2-2*a*x+2)/(a^3))",</tt><br>
<tt></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x^3*exp(a*x),exp(a*x)*x^3/a-3/a*integral(x^2*exp(a*x),x))",</tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"f(x^3*exp(a*x+b),exp(a*x+b)*x^3/a-3/a*integral(x^2*exp(a*x+b),x))",</tt><br>
<tt></tt><br>
<tt>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;NULL,</tt><br>
<tt>};</tt><br>
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